Rigid body physics only applied correctly in edit mode
Thanks @zippy for your answer. I checked the mesh again and have to admit that I missed to look on the scaling properties, although the dimensions were fine, it was scaled by factor 0.013;) Now everything collides fine in object mode, too.
Thus you shouldn't play around at 2 am I think;)
The observed behavior makes completely sense now, because the integration steps for the solver are too far away from each other because of the (actual) size.